{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2023 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# linear_programming_example"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/linear_solver/linear_programming_example.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/ortools/linear_solver/samples/linear_programming_example.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "Linear optimization example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ortools.linear_solver import pywraplp\n",
    "\n",
    "\n",
    "def LinearProgrammingExample():\n",
    "    \"\"\"Linear programming sample.\"\"\"\n",
    "    # Instantiate a Glop solver, naming it LinearExample.\n",
    "    solver = pywraplp.Solver.CreateSolver(\"GLOP\")\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    # Create the two variables and let them take on any non-negative value.\n",
    "    x = solver.NumVar(0, solver.infinity(), \"x\")\n",
    "    y = solver.NumVar(0, solver.infinity(), \"y\")\n",
    "\n",
    "    print(\"Number of variables =\", solver.NumVariables())\n",
    "\n",
    "    # Constraint 0: x + 2y <= 14.\n",
    "    solver.Add(x + 2 * y <= 14.0)\n",
    "\n",
    "    # Constraint 1: 3x - y >= 0.\n",
    "    solver.Add(3 * x - y >= 0.0)\n",
    "\n",
    "    # Constraint 2: x - y <= 2.\n",
    "    solver.Add(x - y <= 2.0)\n",
    "\n",
    "    print(\"Number of constraints =\", solver.NumConstraints())\n",
    "\n",
    "    # Objective function: 3x + 4y.\n",
    "    solver.Maximize(3 * x + 4 * y)\n",
    "\n",
    "    # Solve the system.\n",
    "    print(f\"Solving with {solver.SolverVersion()}\")\n",
    "    status = solver.Solve()\n",
    "\n",
    "    if status == pywraplp.Solver.OPTIMAL:\n",
    "        print(\"Solution:\")\n",
    "        print(f\"Objective value = {solver.Objective().Value():0.1f}\")\n",
    "        print(f\"x = {x.solution_value():0.1f}\")\n",
    "        print(f\"y = {y.solution_value():0.1f}\")\n",
    "    else:\n",
    "        print(\"The problem does not have an optimal solution.\")\n",
    "\n",
    "    print(\"\\nAdvanced usage:\")\n",
    "    print(f\"Problem solved in {solver.wall_time():d} milliseconds\")\n",
    "    print(f\"Problem solved in {solver.iterations():d} iterations\")\n",
    "\n",
    "\n",
    "LinearProgrammingExample()\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 5
}
